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Since high school, I have been rebellious to how physics derivations are presented with difficult and confusing mathematical tools. I am not used to deriving physics laws using the same mathematical tools that our forefathers of physics used (the same found in various physics text books), which I find not only confusing to me but to the entire scientific community who are categorized as the "Silent Majority". I try so much to tackle the problem from a different perspective without using calculus or differential geometry. I use basic math with simple algebra to arrive at the required proof. This book is the culmination of nearly fifteen years of work that I have done to develop this derivation method. I had never expected it would take anything like as long, but I have discovered vastly more than I ever thought possible, and in fact what I have done now touches almost every existing problem in physics. In the early years, I published some papers in the major scientific research journals which were well received but because they had become scattered, I resolved just to keep working quietly until I had finished, and was ready to present everything in a single coherent way. Two years later this book is the result. And with it my hope is to share what I have done with a wide range of scientists and non-scientists as possible. And now that I have finished building the intellectual structure that I describe in this book, it is my hope that those who read these words can share in the excitement I have had in making the discoveries that were involved. In this book you will learn to derive all the known laws of physics from first principles in your own way and fashion not taught in schools and colleges. "Science should be fun"
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Since it was developed, Newton's law of gravitation and many other laws of physics cannot be derived from one grand underlying principle. Deriving Newton's law of gravitation or Einstein general relativity theory, would mean that gravity emerges from something else and that would mean that the only known Newton's law of universal gravity is no longer a fundamental law of physics.Although this might be true, I believe that everything must have an origin. I believe that there is a fundamental universal physical law from which all other known physical laws can be deduced. I also believe that the laws of physics are not picked at random but there exists an underlying principle from which they can be derived with ease. Failure for some minds to grasp this principle doesn't mean that it doesn't exist. Because I was used to deriving and proving formulae in pure math, I didn't like the way the laws of physics were presented to me without proof. A physics tutor would just write down a set of physical laws without proof. There are so many physics books which still do the same thing.Being curious and passionate to finding out how I could derive all the laws of physics from one single equation is proof that this book would have never existed in the first place if had not discovered the hidden principle that underlies all physics.
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
For physics students interested in the mathematics they use, and for math students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation strikes a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
Providing a broad review of many techniques and their application to condensed matter systems, this book begins with a review of thermodynamics and statistical mechanics, before moving onto real and imaginary time path integrals and the link between Euclidean quantum mechanics and statistical mechanics. A detailed study of the Ising, gauge-Ising and XY models is included. The renormalization group is developed and applied to critical phenomena, Fermi liquid theory and the renormalization of field theories. Next, the book explores bosonization and its applications to one-dimensional fermionic systems and the correlation functions of homogeneous and random-bond Ising models. It concludes with Bohm–Pines and Chern–Simons theories applied to the quantum Hall effect. Introducing the reader to a variety of techniques, it opens up vast areas of condensed matter theory for both graduate students and researchers in theoretical, statistical and condensed matter physics.
*Shortlisted for the 2019 Royal Society Insight Investment Science Book Prize* One of the most fascinating scientific detective stories of the last fifty years, an exciting quest for a new form of matter. “A riveting tale of derring-do” (Nature), this book reads like James Gleick’s Chaos combined with an Indiana Jones adventure. When leading Princeton physicist Paul Steinhardt began working in the 1980s, scientists thought they knew all the conceivable forms of matter. The Second Kind of Impossible is the story of Steinhardt’s thirty-five-year-long quest to challenge conventional wisdom. It begins with a curious geometric pattern that inspires two theoretical physicists to propose a radically new type of matter—one that raises the possibility of new materials with never before seen properties, but that violates laws set in stone for centuries. Steinhardt dubs this new form of matter “quasicrystal.” The rest of the scientific community calls it simply impossible. The Second Kind of Impossible captures Steinhardt’s scientific odyssey as it unfolds over decades, first to prove viability, and then to pursue his wildest conjecture—that nature made quasicrystals long before humans discovered them. Along the way, his team encounters clandestine collectors, corrupt scientists, secret diaries, international smugglers, and KGB agents. Their quest culminates in a daring expedition to a distant corner of the Earth, in pursuit of tiny fragments of a meteorite forged at the birth of the solar system. Steinhardt’s discoveries chart a new direction in science. They not only change our ideas about patterns and matter, but also reveal new truths about the processes that shaped our solar system. The underlying science is important, simple, and beautiful—and Steinhardt’s firsthand account is “packed with discovery, disappointment, exhilaration, and persistence...This book is a front-row seat to history as it is made” (Nature).
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Elements of Solid State Physics Second Edition M. N. Rudden and J. Wilson University of Northumbria at Newcastle, Newcastle upon Tyne, UK This textbook provides a basic introduction to the principles of solid state physics and semiconductor devices and will prove essential for first and second year students of physics, materials science and electrical/electronic engineering courses. It assumes no prior knowledge of quantum or statistical mechanics and relies on simple models to illustrate the physical principles. However, the opportunity has been taken in this edition to extend the concept of energy bands to a consideration of E--k curves, and certain new material has been added, notably relating to superconductivity and optoelectronic devices, including lasers, following significant developments in these areas. Elements of Solid State Physics, Second Edition, presents the student with an essentially non-mathematical approach to the subject. Arranged in a logical sequence with many clear illustrations, each chapter has a number of worked examples and discussion points, as well as questions and answers. Readers of this fully revised and updated edition will receive a thorough grounding in the principles of solid state physics and should have sufficient knowledge about modern electronic devices to proceed to more advanced texts in this area. Main Contents: Some Aspects of Modern Physics; Structure of Crystalline Solids; Theories of Conduction and Magnetism; Energy Bands in Solids; Quantum Theory of Conduction; Semiconductor Devices.